Correction:${\mathrm{z}}^{\mathrm{3}}+1\mathrm{=0}$ ${\mathrm{z}}^{\mathrm{3}}\mathrm{=}\mathrm{-}\mathrm{1}$ Since $\left|\mathrm{-}\mathrm{1}\right|\mathrm{<}\left|2\right|$, then ${\mathrm{z}}^{\mathrm{3}}+1$ has 3 zero in $\left|z\right|\mathrm{<2}$

Si Ying, I think there is somthing wrong in your solution, although your answer is correct. You cannot say |z^3+1|=|1^3+1| when|z| = 1 and |z^3+1| = |2^3+1| when |z|=2 because z^3 is not the same as 1^3 or 2^3. They just have the same modulus.See my answer on the scanned picture.